The invention relates to a method and an apparatus for controlling the operation of an internal combustion engine. More particularly, the invention relates to engine control at the so-called lean burning or lean running limit, especially, but not necessarily, when used in conjunction with an electronic fuel injection system which receives data regarding engine speed (rpm) and aspirated air flow rate and which generates fuel control pulses whose duration is related to the amount of fuel to be delivered by electromagnetic fuel supply devices, for example fuel injection valves. Electronic fuel supply systems of this type normally contain a correction circuit (multiplier circuit) so as to permit an adjustment or fine tuning of the duration of the fuel control pulses as a function of further engine variables, for example temperature, altitude, etc. One of the further variables may be in particular the so-called engine roughness defined as being fluctuations in the rotational acceleration of inertial engine members. In a method and an apparatus to which this invention relates particularly, the engine roughness is determined by measuring the fluctuations of the engine speed in three successive crankshaft revolutions. During each period of revolution, a pulse train of a certain counting frequency is supplied to a first up-counter as well as to a third up-counter while twice the counting frequency is supplied to a second, down-counter. At the termination of each crankshaft revolution, the contents of these counters are transferred into the next adjacent counter while the first counter is reset to zero. Subsequently, a comparison is performed between the actual value and a set-point value by transferring the contents of the last up-counter to a totalizing counter and counting the latter down with an rpm-dependent frequency which constitutes the set-point value. The known method and apparatus to which the present invention particularly relates is described in detail in the above-mentioned U.S. Pat. No. 4,044,235. There is described in that patent a digital method for carrying out a lean-burning control of an internal combustion engine in which sequential periods T of engine revolution are measured to form the quantity .DELTA.(.DELTA.T) and to compare this quantity with a predetermined set-point value at the termination of a crankshaft revolution. The number of times which the magnitude of the quantity .DELTA.(.DELTA.T) exceeds the set-point value in one direction or the other is transformed by an integrating member into a proportional DC voltage which is fed to a multiplying circuit within an electric fuel supply system, in particular to an electronic fuel injection system so as to vary the duration of fuel control pulses. When an analog type integrating circuit as described in U.S. Pat. No. 4,044,235 is used, the response time is of the order of seconds. When such a relatively slow acting analog integrating circuit is used in conjunction with a very rapidly operating digital system for lean burning control, there is a certain amount of mismatching because it is not always possible to change the duration of the fuel control pulses fast enough to permit an optimum effect on the drivability of the vehicle equipped with such a system.